A157727 - OEIS

%I #25 Jul 22 2024 09:17:18

%S 4,5,5,6,7,9,12,17,25,38,59,93,148,237,381,614,991,1601,2588,4185,

%T 6769,10950,17715,28661,46372,75029,121397,196422,317815,514233,

%U 832044,1346273,2178313,3524582,5702891,9227469,14930356,24157821,39088173,63245990,102334159

%N a(n) = Fibonacci(n) + 4.

%H Vincenzo Librandi, <a href="/A157727/b157727.txt">Table of n, a(n) for n = 0..285</a>

%H Ivana Jovović and Branko Malešević, <a href="http://nntdm.net/volume-23-2017/number-1/28-38/">Some enumerations of non-trivial composition of the differential operations and the directional derivative</a>, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F a(0) = 4, a(1) = 5, a(n) = a(n - 2) + a(n - 1) - 4. - _Reinhard Zumkeller_, Jul 30 2013

%F G.f.: (4 - 3*x - 5*x^2)/((1 - x)*(1 - x - x^2)). - _Stefano Spezia_, Jul 21 2024

%t Fibonacci[Range[0,50]]+4 (* _Harvey P. Dale_, Jun 17 2011 *)

%o (Magma) [ Fibonacci(n) + 4: n in [0..40] ]; // _Vincenzo Librandi_, Apr 24 2011

%o (PARI) a(n)=fibonacci(n)+4 \\ _Charles R Greathouse IV_, Jul 02 2013

%o (Haskell)

%o a157727 = (+ 4) . a000045

%o a157727_list = 4 : 5 : map (subtract 4)

%o                        (zipWith (+) a157727_list $ tail a157727_list)

%o -- _Reinhard Zumkeller_, Jul 30 2013

%Y Cf. A000045, A001611, A000071, A157725, A001911, A157726, A006327, A157727, A157728, A157729, A167616.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Jun 26 2010